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Efficiency is a function of a transformer's power losses, but it's easy to lose sight of what transformer efficiency means in the real world.
Last month, we discussed transformer voltage regulation. Closely related to that concept is transformer efficiency. You calculate this the same way you calculate efficiency for other equipment: Divide the output by the input. If you multiply the result by 100, you can show this number as a percentage.
Efficiency is a function of a transformer's power losses, and two factors account for nearly all of these losses. One is winding copper loss. Since you have two sets of windings, you have two components to copper loss: primary and secondary winding copper loss.
The second factor accounting for transformer power losses is core loss. You get core losses due to hysteresis - a function of several characteristics of the core steel (or iron), all determined by the manufacturing process. Fortunately, the core losses for any given transformer stay constant (provided supply frequency is constant). You obtain maximum efficiency when winding copper loss equals core loss.
To calculate transformer efficiency in any condition other than no-load, you must first calculate the equivalent resistance (ER) of both the primary and secondary (including the load). The effort needed to arrive at the ER (which changes with facility reconfigurations) is hard to justify for typical applications.
Nonetheless, you can easily calculate no-load efficiency. First, multiply the output voltage by the output current (for load conditions, you would multiply the result by the cosine of the ER). Repeat this step for the input. Then, divide the output results by the input results. No-load efficiency gives you a basis for comparing transformers or testing a transformer against a specification. It won't tell you how efficient your transformer is when in use. That's why we still - at least in theory - calculate transformer efficiency in conditions other than no-load. Yet, the no-load calculation - because it is so easy - is often worthwhile. For example, you first establish a baseline for each transformer. When you experience problems that indicate a transformer malfunction, recalculating no-load efficiency again can shorten troubleshooting time dramatically.
Does the transformer efficiency, under load conditions, have any real value to you? Yes, if you can calculate the ER of everything on the load side - something few installations merit paying for. Thus, in the real world, we go back to the basic rule of thumb for maximizing transformer efficiency: Load the transformer to about 80% of capacity. In a lightly loaded transformer, the equivalent secondary resistance will not bring the winding and core losses anywhere close.
Once you load a transformer properly, you can safely assume it will run as efficiently as it's going to run. Now, just ensure it has proper cooling and is not subject to excessive harmonics. If you have problems with efficiency or voltage regulation, don't automatically upgrade to a larger or K-rated transformer. On the other hand, once you have the proper loading and cooling, you'll have eliminated key variables so an upgrade is easier to justify.
Don't jump into a purchase of harmonics mitigation equipment either. Inspect the grounding and bonding system from the transformer to the service entrance. This will often reveal the source of your problem.